| Title:
|
Distinguished connections on $(J^{2}=\pm 1)$-metric manifolds (English) |
| Author:
|
Etayo, Fernando |
| Author:
|
Santamaría, Rafael |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
52 |
| Issue:
|
3 |
| Year:
|
2016 |
| Pages:
|
159-203 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We study several linear connections (the first canonical, the Chern, the well adapted, the Levi Civita, the Kobayashi-Nomizu, the Yano, the Bismut and those with totally skew-symmetric torsion) which can be defined on the four geometric types of $(J^2=\pm 1)$-metric manifolds. We characterize when such a connection is adapted to the structure, and obtain a lot of results about coincidence among connections. We prove that the first canonical and the well adapted connections define a one-parameter family of adapted connections, named canonical connections, thus extending to almost Norden and almost product Riemannian manifolds the families introduced in almost Hermitian and almost para-Hermitian manifolds in [13] and [18]. We also prove that every connection studied in this paper is a canonical connection, when it exists and it is an adapted connection. (English) |
| Keyword:
|
$(J^2=\pm 1)$-metric manifold |
| Keyword:
|
$\alpha $-structure |
| Keyword:
|
natural connection |
| Keyword:
|
Nijenhuis tensor |
| Keyword:
|
second Nijenhuis tensor |
| Keyword:
|
Kobayashi-Nomizu connection |
| Keyword:
|
first canonical connection |
| Keyword:
|
well adapted connection |
| Keyword:
|
connection with totally skew-symmetric torsion |
| Keyword:
|
canonical connection |
| MSC:
|
53C05 |
| MSC:
|
53C07 |
| MSC:
|
53C15 |
| MSC:
|
53C50 |
| idZBL:
|
Zbl 06644065 |
| idMR:
|
MR3553174 |
| DOI:
|
10.5817/AM2016-3-159 |
| . |
| Date available:
|
2016-09-20T11:58:21Z |
| Last updated:
|
2018-01-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145830 |
| . |
| Reference:
|
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| Reference:
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